Measurement of topological invariants in a 2D photonic system

By S. Mittal, S. Ganeshan, Jingyun Fan, Abolhassan Vaezi, M. Hafezi. Nature Photonics, 2015

180 citations recorded by the source corpus.

A photonic analogue of charge pumping in electronic quantum Hall systems is demonstrated by using a finite 2D square annulus of ring resonators. Topological invariants are investigated by observing the shift of the edge state resonances. A hallmark feature of topological physics is the presence of one-way propagating chiral modes at the system boundary1,2. The chirality of edge modes is a consequence of the topological character of the bulk. For example, in a non-interacting quantum Hall model, edge modes manifest as mid-gap states between two topologically distinct bulk bands. The bulk–boundary correspondence dictates that the number of chiral edge modes, a topological invariant called the winding number, is completely determined by the bulk topological invariant, the Chern number3. Here, for the first time, we measure the winding number in a 2D photonic system. By inserting a unit flux quantum at the edge, we show that the edge spectrum resonances shift by the winding number. This experiment provides a new approach for unambiguous measurement of topological invariants, independent of the microscopic details, and could possibly be extended to probe strongly correlated topological orders.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/4ca17ffac1e5490d529fd43fddcb9dca9b07bc4d

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Citations in the corpus

Artificial gauge fields in materials and engineered systems (2017, unknown): “Moreover, this setting facilitated the first Chern number measurement in a truly 2D photonic system, exploiting the bulk-edge correspondence [193].”
Topological Photonic Crystals: Physics, Designs, and Applications (2022, background): “Up to now, topological phenomena have been proposed and realized in diverse photonic systems, including photonic crystals (PCs) [16-25], plasmonic systems [18-29], metamaterials [30-42], coupled resonator optical waveguides [43-53], waveguide arrays [54-66], microcavity polaritonic systems [67-74], ”
Topological photonics (2018, methodology): “A.4) was experimentally studied by Mittal et al. (2016).”
Synthetic dimensions in integrated photonics: From optical isolation to four-dimensional quantum Hall physics (2015, background): “The use of a synthetic dimension has two key advantages over this experiment; first, the gauge field can be controlled externally through the phase of the dielectric modulation that induces the intermode coupling, whereas with link resonators, the gauge field is almost fixed at the time of fabricati”
Exciton-polaritons in lattices: A non-linear photonic simulator (2016, background): “At the classical level, photonic simulators have played a key role in the implementation of artificial gauge fields for neutral particles, and have allowed the experimental investigation of Anderson localisation [5], topological insulators [6,7], quantum spin- [8,9] and the anomalous Hall effect [10”
Keldysh field theory for driven open quantum systems (2015, background): “[329] Sunil Mittal, Sriram Ganeshan, Jingyun Fan, Abolhassan Vaezi, and Mohammad Hafezi, “Measurement of topological invariants in a 2d photonic system,” Nature Photonics 10, 180 (2016).”
Topological insulator laser: Theory (2018, background): “The second relies on an aperiodic array architecture that creates an artificial magnetic field, as was demonstrated experimentally in passive systems (silicon) (8, 12, 13, 37).”
Realization of an anomalous Floquet topological system with ultracold atoms (2020, background): “[19] S.”